Mike, I'd recommend you do a search on "tiltmeters" and you'll find a great deal of information on this topic. Many of us have bought tiltmeters from Rick at R&B Mfg. and he has a great deal of experience that he's shared with us.
As far as I know, none of the tractor manufacturers publish a figure for maximum angle of operation, although I believe Rick said there is a standard requiring 20 degrees. The big problem is that if you are operating at 20 degrees, the slightest soft spot on the low side, or hump, rock, stump, stick, etc. on the high side will change it so fast that you may go over before you know what happened. 18 degrees is the most I've tried, and 15 degrees scares the dickens out of me. Of course, I'm talking about side to side slope, and think straight up or down 15 to 25 would not be a major worry if you can get enough traction. However, I only recently added a tiltmeter for front to rear and haven't really been on steep enough slopes to give a good answer yet.
Bird